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The key point is that we should generate the palindromes instead of enumerating all the numbers and checking if each one of them is palindrome. Since the number<=10^8, we only need to generate 10^4 palindromes. This is a great performance boost comparing to 10^8.

Lession Learned:
1. To generate palindrome, there is no need to enumerate range for each digit. We may just try [0, 9999]. I never think of this.
2. We should balance between performance and code complexity. For example, generating palindromes can boost performance a lot. However, I also tried to filter numbers<a or >b as special cases, but this performance care increases my code compexity a lot. I may just checking this after completing the numbers. 
3. It seems that I am the only one use the DFS for this problem because I hate hard-coding.
4. During enumerating through an array, always use sizeof(arr)/sizeof(item_size) as upper limit. This will save you a lot of time during refactoring.
5. How to implement the "atoi":

int atoi(char str[], int len)
{
 assert(arr!=NULL);
 assert(len>0);

 int number=0;
 for(int j=0;j<len;j++)
 {
  number*=10;
  number+=(str[j]-'0');
 }
 return number;
}